<MHO> [My wife] just informed me that this year, July has five
Fridays, five Saturdays and five Sundays. This only happens every 800
or so years.

<MHO> Calendar geeks, rejoice!

He made the mistake of invoking the Calendar Geeks, so here I am,
ready to assist!

First, I note that any weird calendar event that occurs, will recur in
no more than 400 years, because the Gregorian calendar repeats in a
400-year cycle and 400 Gregorian years is also an exact multiple of 7
days. (It is 400·365 days + (100 - 4 + 1) leap days = 146,097
days, which is exactly 20,871 weeks.) So it is impossible that the
event could be as rare as once every 800 or so years. If it happens
in 2011, then it happened in 1611 (in Catholic countries) and it will
happen in 2411 also.

Now in the particular case cited by MHO, it's clear that since the
length of July doesn't vary, the number of Fridays, Saturdays or
Sundays depends only on the day of the week on which July 1 falls.
You get five Fridays, Saturdays, and Sundays whenever July 1 falls on
a Friday. Common sense suggests that this should happen about 1/7 of
the time, and so around every 7 years, not every 800, or even every
400 years. And in fact it last occurred in 2005, and will occur next
in 2016.

[ Addendum 20110527: It turns out this is actually a Thing; there is even
a Snopes
page about it. People will tweet almost anything, it seems. ]